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Simplifying 4x * log[4](2x + -1) + 3log[4](2x + -1) = 0 Reorder the terms: 4x * glo * 4(-1 + 2x) + 3log[4](2x + -1) = 0 Reorder the terms for easier multiplication: 4 * 4x * glo(-1 + 2x) + 3log[4](2x + -1) = 0 Multiply 4 * 4 16x * glo(-1 + 2x) + 3log[4](2x + -1) = 0 Multiply x * glo 16glox(-1 + 2x) + 3log[4](2x + -1) = 0 (-1 * 16glox + 2x * 16glox) + 3log[4](2x + -1) = 0 (-16glox + 32glox2) + 3log[4](2x + -1) = 0 Reorder the terms: -16glox + 32glox2 + 3glo * 4(-1 + 2x) = 0 Reorder the terms for easier multiplication: -16glox + 32glox2 + 3 * 4glo(-1 + 2x) = 0 Multiply 3 * 4 -16glox + 32glox2 + 12glo(-1 + 2x) = 0 -16glox + 32glox2 + (-1 * 12glo + 2x * 12glo) = 0 -16glox + 32glox2 + (-12glo + 24glox) = 0 Reorder the terms: -12glo + -16glox + 24glox + 32glox2 = 0 Combine like terms: -16glox + 24glox = 8glox -12glo + 8glox + 32glox2 = 0 Solving -12glo + 8glox + 32glox2 = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-3 + 2x + 8x2) = 0 Factor a trinomial. 4glo((-3 + -4x)(1 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Add '4x' to each side of the equation. -4x + 4x = 3 + 4x Combine like terms: -4x + 4x = 0 0 = 3 + 4x Simplifying 0 = 3 + 4x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Add '2x' to each side of the equation. -2x + 2x = -1 + 2x Combine like terms: -2x + 2x = 0 0 = -1 + 2x Simplifying 0 = -1 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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